Finite Group Databasebeta

C3×C2339 #20296273

order7017
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C7×C167 (order 4676) · Inn(G) = C1 · Out(G) = C22×C7×C167
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7017
abelianC3×C2339

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7017 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7017, Dic7017, D3×D2339, …
Fitting subgroup ofD3×C2339, C3×D2339, D7017, …
socle ofD3×C2339, C3×D2339, D7017, …
maximal subgroup ofD3×C2339, C3×D2339, D7017, …
maximal normal subgroup ofD3×C2339, C3×D2339, D7017, …
maximal quotient ofC2×C3×C2339, C9×C2339, C32×C2339, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7017, 1);